Properties

Label 126.3.s
Level $126$
Weight $3$
Character orbit 126.s
Rep. character $\chi_{126}(53,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $72$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(126, [\chi])\).

Total New Old
Modular forms 112 8 104
Cusp forms 80 8 72
Eisenstein series 32 0 32

Trace form

\( 8 q + 8 q^{4} + 12 q^{7} + O(q^{10}) \) \( 8 q + 8 q^{4} + 12 q^{7} + 16 q^{10} + 56 q^{13} - 16 q^{16} - 20 q^{19} + 32 q^{22} - 60 q^{25} - 48 q^{28} - 100 q^{31} + 32 q^{34} + 76 q^{37} - 32 q^{40} - 248 q^{43} - 112 q^{46} + 44 q^{49} + 56 q^{52} + 176 q^{55} + 160 q^{58} - 64 q^{61} - 64 q^{64} + 108 q^{67} - 160 q^{70} + 60 q^{73} - 80 q^{76} - 364 q^{79} + 96 q^{82} + 224 q^{85} + 32 q^{88} + 404 q^{91} + 192 q^{94} + 480 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
126.3.s.a \(4\) \(3.433\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-14\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}+(-7+\cdots)q^{7}+\cdots\)
126.3.s.b \(4\) \(3.433\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(26\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+\beta _{1}q^{5}+(5+3\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)